9x^2+51x-20=-2

Solution for 9x^2+51x-20=-2 equation:

Simplifying
9x2 + 51x + -20 = -2

Reorder the terms:
-20 + 51x + 9x2 = -2

Solving
-20 + 51x + 9x2 = -2

Solving for variable 'x'.

Reorder the terms:
-20 + 2 + 51x + 9x2 = -2 + 2

Combine like terms: -20 + 2 = -18
-18 + 51x + 9x2 = -2 + 2

Combine like terms: -2 + 2 = 0
-18 + 51x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 17x + 3x2) = 0

Factor a trinomial.
3((-6 + -1x)(1 + -3x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-6, 0.3333333333}